UK: IFRS 9 Methodology Arbitrage

Introduction

Our previous article "
IFRS 9: What to expect of an expectation" generated
significantly more interest and feedback than usual. In this
article we explore some of the common themes from respondents'
correspondence, and explore whether firms' methodological
choices lead to arbitrage opportunities in the market.

We would like to first extend our thanks to everyone who took
the time to send their comments (publicly as well as privately).
Correspondence focused on three important themes, which we discuss
below:

Scenario Design;

How to estimate probabilities of loss
data points; and

The principle of parsimony;

We then explore whether firms' methodological choices lead
to arbitrage opportunities for market participants.

Scenario Design

The IFRS 9 standard (as well as any credit manager looking to
quantify and price risk) is interested in the expectation of a
distribution of possible credit losses. The random variable of
interest is credit loss, and by definition the expectation requires
integration over the distribution of credit loss, as illustrated in
our previous article. We labelled the loss data points as (credit
loss quantum, cumulative likelihood of that loss occurring) and
sought to interpolate the underlying distribution in order to
recover the expectation.

A common misconception is that the scenarios themselves require
probabilities to be assigned. Whilst many banks are accustomed to
terminology to the effect of a "1 in 10 scenario", this
would only correspond to a 1-in-10 credit loss severity in the
event that a monotonic relationship exists between quantiles of
scenario (however that may be measured) and quantiles of credit
loss. It can be proven that this relationship is not monotonic, and
the result is intuitive. A particularly severe recession followed
by a recovery would in-effect "take out" losses from the
reporting date balance sheet early (and in the limiting case, wipe
out the entire book) to the extent that quantiles of GDP,
unemployment or bond spread in the outer years have next to zero
impact on overall credit losses for that scenario.

Techniques exist for generating plausible macro paths by
historically observed (or indeed any defined) exogenous shocks onto
current conditions. Such techniques have the attractive properties
of being explainable and reasonably objective. Whilst it may be
reasonable to assume that such-and-such a macro outturn might occur
once every X years, we reiterate the fact that P(scenario) does not
align to P(credit loss) in the general case.

In the next section, we explore whether probabilities can, or
indeed should, be assigned at all.

Probabilities

In our previous article, we invoked an assumption that the data
points being input into the interpolations are precise (i.e. they
can be treated as free parameters in the overall ECL model). We
mentioned that in practice the cumulative probability of each loss
data point cannot be determined with anything near certainty. In
this section, we discuss this assumption further.

The only thing that can be said with certainty about
each loss data point, is that its probability of occurring lies
between 0 and 1. With zero historical data points for a given
scenario, this leads us to the intuitive result that the cumulative
probability for a given loss data point can only be set by human
judgement. Perhaps unsurprisingly, the judgment around "was
this loss a 1-in-10, or a 1-in-7, or maybe a 1-in-12" is
highly subjective, and leads to such large variance in estimates of
probabilities, that they cannot be treated as free parameters in
the model. We would need to model another layer of distributions
– the distribution of plausible values for each loss data
point's probability. From a scientific perspective, this kind
of model is unidentifiable – akin to an unobservable black
box. Thus, it is a mathematical certainty that use of subjective
probability inputs to ECL calculations will lead to bias.

An alternative is to use time-series techniques to model future
uncertainty, and solve for the distribution of credit losses. In
the next section, we explore whether this would lead to a
"better" model.

The Principle of Parsimony

Said the philosopher William of Ockham, "Frustra fit per
plura quod potest fieri per pauciora" – it is futile to
do with more what can be done with less. In the modern application
of scientific and statistical theory, we are perhaps more familiar
with the principle of parsimony: We tend to favour selecting the
model that fits best, with the least complexity, and use measures
of complexity-adjusted goodness-of-fit to compare candidate
models.

Metrics such as the Akaike Information Criterion (AIC) and
Bayesian Information Criterion (BIC) have achieved widespread
acceptance in the scientific community as a means of applying a
"penalty" to pure goodness-of-fit, in proportion to the
number of free parameters in each model.

The additional free parameters
required to estimate hazard curves may (or may not) outweigh any
improvement in goodness-of-fit with respect to a Markovian
migration assumption;

The additional free parameters
required in the use of cubic splines may (or may not) outweigh any
improvement in goodness-of-fit with respect to having simply binned
the explanatory variables; or

The additional free parameter
required to model rating-level cyclicality (sometimes referred to
as "PITness") may (or may not) outweigh any improvement
in goodness-of-fit with respect to having assumed that ratings are
100% through-the-cycle.

Returning to the use of fixed scenarios, it is reasonable to ask
how the AIC or BIC might compare with time series techniques seen
in the sciences, engineering and econometric applications. Two
plausible interpretations present themselves:

A strict interpretation would be that
the fixed scenario approach does not model randomness. Therefore,
the likelihood of any macro outturn that does not perfectly match a
given scenario is precisely zero.

A less-strict interpretation would be
that the randomness has been shifted to the uncertainty in the
probability of the loss associate with a scenario. As discussed
above, the parameters of this model are unidentifiable and
likelihood therefore cannot be computed.

Conclusions

To summarise, we have discussed:

Use of scenario probabilities being
mathematically inconsistent with loss probabilities;

Loss probabilities cannot be
estimated with any certainty; and

Use of distributional modelling
approaches may lead to better complexity-adjusted goodness-of
fit.

It would be easy to surmise that many IFRS 9 models are not fit
for purpose. We therefore draw particular attention to the fact
that the IFRS 9 standard only requires unbiased estimates.
Minimum-variance and parsimony are not mentioned, leaving
significant scope for firms to achieve material compliance with
approaches that are, mathematically, sub-optimal.

Lastly, we pose the question of what if materially-compliant yet
mathematically sub-optimal estimates are also market-inconsistent?
In this situation, market participants could in-effect trade away
excess impairment in the banking system until arbitrage
opportunities disappear, releasing balance sheet to support lending
growth and, ultimately, the macro-economy.

The content of this article is intended to provide a general
guide to the subject matter. Specialist advice should be sought
about your specific circumstances.

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